On Weighted Inductive Limits of Spaces of Continuous Function.
Nous établissons des résultats d’interpolation non-standards entre les espaces de Besov et les espaces et , avec des applications aux lemmes de régularité en moyenne et aux inégalités de type Gagliardo-Nirenberg. La preuve de ces résultats utilise les décompositions dans des bases d’ondelettes.
We give a new perspective on the homological characterizations of amenability given by Johnson & Ringrose in the context of bounded cohomology and by Block & Weinberger in the context of uniformly finite homology. We examine the interaction between their theories and explain the relationship between these characterizations. We apply these ideas to give a new proof of non-vanishing for the bounded cohomology of a free group.
In this note we exhibit points of weak*-norm continuity in the dual unit ball of the injective tensor product of two Banach spaces when one of them is a G-space.